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Mathematical Optimization for Data Science Group
Department of Mathematics and Computer Science, Saarland University, Germany
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Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation |
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Abstract: We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones derived from a (deterministic) worst-case analysis. The results rely on PAC-Bayesian bounds for general, possibly unbounded loss-functions based on exponential families. Then, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum. Furthermore, we provide a concrete algorithmic realization of the framework and new methodologies for learning-to-optimize, and we conduct four practically relevant experiments to support our theory. With this, we showcase that the provided learning framework yields optimization algorithms that provably outperform the state-of-the-art by orders of magnitude. |
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Bibtex 
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Latest update: 04.04.2024 |
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Citation: M. Sucker, J. Fadili, P. Ochs: Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation. ![[pdf]](/images/pdf_14x14.png) Technical Report, ArXiv e-prints, arXiv:2404.03290, 2024. |
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Bibtex: @techreport{SFO24, title = {Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation}, author = {M. Sucker and J. Fadili and P. Ochs}, year = {2024}, journal = {ArXiv e-prints, arXiv:2404.03290}, } |
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